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Optimization · Everything Else

Bruno Mlodozeniec, Pierre Ablin, Louis Béthune, Dan Busbridge, Michal Klein, Jason Ramapuram, marco cuturi

Hyperparameter tuning can dramatically impact training stability of large-scale models. Recent works on neural network parameterisations, such as μP, have shown that layer types and sizes should dictate how global hyperparameters should be rescaled in order to achieve efficient transfer across model sizes. On the other hand, the established practice for hyperparameter optimisation search is to look for optimal global base values that apply at some fixed model scale. We transfer hyperparameters across all scaling axes: width and depth, using an extension of CompleteP (Dey et al., 2025), training horizon, and batch size. Our study covers all optimisation hyperparameters of modern models: learning rates, Adam parameters, weight decay, initialisation scales, and residual block multipliers. Lastly, we demonstrate that hyperparameter transfer holds even in the per-layer hyperparameter regime. We characterise the empirical challenges of navigating the high-dimensional hyperparameter landscape, and propose practical guidelines for tackling this optimisation problem. We suggest a simplified parameterisation of the hyperparameter space that reduces the dimensionality of the search-space at no performance cost. Our experiments demonstrate training speed improvements when applying transferred hyperparameters to Large Language Models.

Computer Vision · Vision Models & Multimodal

Or Hirschorn, Shai Avidan

Category-Agnostic Pose Estimation (CAPE) localizes keypoints across diverse object categories with a single model, using one or few annotated support images. Recent works have shown that using a pose-graph (i.e., treating keypoints as nodes in a graph rather than isolated points) helps handle occlusions and break symmetry. However, these methods assume a given pose-graph with equal-weight edges, leading to suboptimal results. We introduce EdgeCape, a novel framework that overcomes these limitations by predicting the graph's edge weights in order to optimize localization. To further leverage structural (i.e., graph) priors, we propose integrating Markov Attention Bias, which modulates the self-attention interaction between nodes based on the number of hops between them. We show that this improves the model’s ability to capture global spatial dependencies. Evaluated on the MP-100 benchmark, which includes 100 categories and over 20K images, EdgeCape achieves state-of-the-art results in the 1-shot and 5-shot settings, significantly improving keypoint localization accuracy.

Wei Bu

Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(\theta)/g} d\theta$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

Theory · Domain Adaptation and Transfer Learning

aodi Li, Liansheng Zhuang, Xiao Long, Houqiang Li, Shafei Wang

This paper explores the geometric characteristics of loss landscapes to enhance domain generalization (DG) in deep neural networks. Existing methods mainly leverage the local flatness around minima for improved generalization. However, recent theoretical studies indicate that flatness does not universally guarantee better generalization. Instead, this paper investigates a global geometrical property for domain generalization, i.e., \emph{mode connectivity}, the phenomenon where distinct local minima are connected by continuous low-loss pathways. Different from flatness, mode connectivity enables transitions from poor to superior generalization models without leaving low-loss regions. To navigate these connected pathways effectively, this paper proposes a novel Billiard Optimization Algorithm (BOA), which discovers superior models by mimicking billiard dynamics. During this process, BOA operates within a low-dimensional Krylov subspace, aiming to alleviate the curse of dimensionality caused by the high-dimensional parameter space of deep models. Furthermore, this paper reveals that oracle test gradients strongly align with the Krylov subspace constructed from training gradients across diverse datasets and architectures. This alignment offers a powerful tool to bridge training and test domains, enabling the efficient discovery of superior models with limited training domains. Experiments on DomainBed demonstrate that BOA consistently outperforms existing sharpness-aware and DG methods across diverse datasets and architectures. Impressively, BOA even surpasses the sharpness-aware minimization by 3.6\% on VLCS when using a ViT-B/16 backbone.

Deep Learning · Algorithms

Rahul Thomas, Arka Pal

Speculative sampling reduces the latency of autoregressive decoding for target model LLMs without sacrificing inference quality, by using a cheap draft model to suggest a candidate token and a verification criterion to accept or resample this token. To improve acceptance and decoding efficiency, recent work has explored the multi-draft extension, where at each step $n$ draft tokens are generated, and the verification criterion is a distribution conditioned on these. When this criterion maximizes the probability of accepting some draft token, it is called the optimal transport (OT). However, finding the OT is difficult, as it is the solution of a linear program (OTLP) in over $V^n$ variables, with $V$ being the vocabulary size. Two recent theoretical works have reframed the OTLP in terms of importance sampling or subset selection. In this work, we prove that these formulations are equivalent to an exponentially large relaxed OTLP, so it remains infeasible to solve. Then, we reverse engineer subset selection to formulate the OTLP as a max-flow problem. With a novel application of polymatroid theory, we reduce the exponentially large OTLP to a convex optimization problem in at most $V$ variables. This allows us to devise an algorithm for optimal $n$-draft speculative sampling when the $n$ tokens are chosen i.i.d. from a single draft model, which can be tuned to arbitrary accuracy. Finally, we measure acceptance rates and algorithm runtimes for various $n$ and top-$k$ draft sampling settings. Our findings give the first multi-draft algorithm with 90\% acceptance and under 100 ms of overhead per generated token with negligible deviation from the target model distribution.

Optimization · Learning for Optimization

Xinyu Yuan, Yan Qiao, Zonghui Wang, Wenzhi CHEN

The multi-commodity flow (MCF) problem is a fundamental topic in network flow and combinatorial optimization, with broad applications in transportation, communication, and logistics, etc. Nowadays, the rapid expansion of allocation systems has posed challenges for existing optimization engines in balancing optimality and tractability. In this paper, we present Pram, the first ML-based method that leverages the reasoning power of multimodal language models (MLMs) for addressing the trade-off dilemma—a great need of service providers. As part of our proposal, Pram (i) quickly computes high-quality allocations by dividing the original problem into local subproblems, which are then resolved by an MLM-powered "agent", and (ii) ensures global consistency by harmonizing these subproblems via a multi-agent reinforcement learning algorithm. Theoretically, we show that Pram, which learns to perform gradient descent in context, provably converges to the optimum within the family of MCF problems. Empirically, on real-world datasets and public topologies, Pram achieves performance comparable to, and in some cases even surpassing, linear programming solvers (very close to the optimal solution), and substantially lower runtimes (one to two orders of magnitude faster). Moreover, Pram exhibits strong robustness (<10\% performance degradation under failures or bursts), demonstrating MLM's generalization ability to unforeseen events. Pram is objective-agnostic and seamlessly integrates with mainstream allocation systems, providing a practical and scalable solution for future networks.

Shahaf Bassan, Xuanxiang Huang, Guy Katz

Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and (2) *contrastive reasons*, which are subsets of input features that, when modified, alter a prediction. Prior studies have examined these explanations in different contexts, such as non-probabilistic versus probabilistic frameworks and local versus global settings. In this study, we introduce a unified framework for analyzing these explanations, demonstrating that they can all be characterized through the minimization of a unified probabilistic value function. We then prove that the complexity of these computations is influenced by three key properties of the value function: (1) *monotonicity*, (2) *submodularity*, and (3) *supermodularity* - which are three fundamental properties in *combinatorial optimization*. Our findings uncover some counterintuitive results regarding the nature of these properties within the explanation settings examined. For instance, although the *local* value functions do not exhibit monotonicity or submodularity/supermodularity whatsoever, we demonstrate that the *global* value functions do possess these properties. This distinction enables us to prove a series of novel polynomial-time results for computing various explanations with provable guarantees in the global explainability setting, across a range of ML models that span the interpretability spectrum, such as neural networks, decision trees, and tree ensembles. In contrast, we show that even highly simplified versions of these explanations become NP-hard to compute in the corresponding local explainability setting.

Applications · Robotics

Zicheng Zhang, Ke Wu, Xiangting Meng, Keyu Liu, Jieru Zhao, Wenchao Ding

Monocular 3D Gaussian Splatting SLAM suffers from critical limitations in time efficiency, geometric accuracy, and multi-view consistency. These issues stem from the time-consuming $\textit{Train-from-Scratch}$ optimization and the lack of inter-frame scale consistency from single-frame geometry priors. We contend that a feed-forward paradigm, leveraging multi-frame context to predict Gaussian attributes directly, is crucial for addressing these challenges. We present Flash-Mono, a system composed of three core modules: a feed-forward prediction frontend, a 2D Gaussian Splatting mapping backend, and an efficient hidden-state-based loop closure module. We trained a recurrent feed-forward frontend model that progressively aggregates multi-frame visual features into a hidden state via cross attention and jointly predicts camera poses and per-pixel Gaussian properties. By directly predicting Gaussian attributes, our method bypasses the burdensome per-frame optimization required in optimization-based GS-SLAM, achieving a $\textbf{10x}$ speedup while ensuring high-quality rendering. The power of our recurrent architecture extends beyond efficient prediction. The hidden states act as compact submap descriptors, facilitating efficient loop closure and global $\mathrm{Sim}(3)$ optimization to mitigate the long-standing challenge of drift. For enhanced geometric fidelity, we replace conventional 3D Gaussian ellipsoids with 2D Gaussian surfels. Extensive experiments demonstrate that Flash-Mono achieves state-of-the-art performance in both tracking and mapping quality, highlighting its potential for embodied perception and real-time reconstruction applications.

Computer Vision · Image and Video Generation

Jianzong Wu, Liang Hou, Haotian Yang, Ye Tian, Pengfei Wan, Di ZHANG, Yunhai Tong

The quadratic complexity of full attention mechanisms poses a significant bottleneck for Video Diffusion Models (VDMs) aiming to generate long-duration, high-resolution videos. While various sparse attention methods have been proposed, many are designed as training-free inference accelerators or do not optimally capture the unique spatio-temporal characteristics inherent in video data when trained natively. This paper introduces Video Mixture of Block Attention (VMoBA), a novel sparse attention mechanism specifically adapted for VDMs. Motivated by an in-depth analysis of attention patterns within pre-trained video transformers, which revealed strong spatio-temporal locality, varying query importance, and head-specific concentration levels, VMoBA enhances the original MoBA framework with three key modifications: (1) a layer-wise recurrent block partition scheme (1D-2D-3D) to dynamically adapt to diverse spatio-temporal attention patterns and improve efficiency; (2) global block selection to prioritize the most salient query-key block interactions across an entire attention head; and (3) threshold-based block selection to dynamically determine the number of attended blocks based on their cumulative similarity. Extensive experiments demonstrate that VMoBA significantly accelerates the training of VDMs on longer sequences, achieving 2.92$\times$ FLOPs and 1.48$\times$ latency speedup, while attaining comparable or even superior generation quality to full attention. Furthermore, VMoBA exhibits competitive performance in training-free inference, offering 2.40$\times$ FLOPs and 1.35$\times$ latency speedup for high-res video generation.

Theory · Reinforcement Learning and Planning

Bowen Hu, Yixin Tao

We study a principal-agent problem in a Markov Decision Process where the principal provides subsidies to influence the agent's policy, which in turn determines the accrued rewards. Our focus is on designing a robust subsidy scheme that maximizes the principal’s cumulative expected return, even when the agent displays bounded rationality and may deviate from the optimal action policy after receiving subsidies. As a baseline, we first analyze the case of a perfectly rational agent and show that the principal’s optimal subsidy coincides with the policy that maximizes social welfare, the sum of the utilities of both the principal and the agent. We then introduce a bounded-rationality model: the globally $\epsilon$-incentive-compatible agent, who accepts any policy whose expected cumulative utility lies within $\epsilon$ of the personal optimum. In this setting, we prove that the optimal robust subsidy scheme problem simplifies to a one-dimensional concave optimization, revealing that optimal subsidies concentrate along social-welfare-maximizing trajectories. We also bound the associated loss in social welfare. Finally, we investigate a finer-grained, state-wise $\epsilon$-incentive-compatible model. In this setting, we show that under two natural definitions of state-wise incentive-compatibility, the problem becomes intractable: one definition results in a non-Markovian agent action policy, while the other renders the search for an optimal subsidy scheme NP-hard.

Optimization · Everything Else

Ruobing Wang, Xin Li, Mingzhong Wang

We propose MILPnet, a multi-scale hybrid attention framework that models Mixed Integer Linear Programming (MILP) problems as geometric sequences rather than graphs. This approach directly addresses the challenge of Foldable MILP instances, a class of problems that graph-based models, specifically Graph Neural Networks (GNNs), fail to distinguish due to expressiveness limits imposed by the Weisfeiler-Lehman test. By representing MILPs through sequences of constraint and objective features, MILPnet captures both local and global geometric structure using a theoretically grounded multi-scale attention mechanism. We theoretically prove that MILPnet can approximate feasibility, optimal objective value, and optimal solution mappings over a measurable topological space with arbitrarily small error. Empirically, MILPnet outperforms graph-based methods in feasibility prediction accuracy and convergence speed on Foldable MILPs, while using significantly fewer parameters. It also generalizes effectively among problem scales and demonstrates strong performance on real-world MILP benchmarks when integrated into an end-to-end solver pipeline. Our code is available.

Reinforcement Learning · Deep RL

Chenghua Huang, Lu Wang, Fangkai Yang, Pu Zhao, Qingwei Lin, Dongmei Zhang, Saravan Rajmohan

In this paper, we explore how directly pretraining a value model simplifies and stabilizes reinforcement learning from human feedback (RLHF). In reinforcement learning, value estimation is the key to policy optimization, distinct from reward supervision. The value function predicts the \emph{return-to-go} of a partial answer, that is, how promising the partial answer is if it were continued to completion. In RLHF, however, the standard pipeline first pretrains a reward model and then learns a value function online, even though no new reward signals are available once preference data is collected. This makes critic learning redundant, as the process of training a reward model and then deriving a value model is informationally equivalent to directly pretraining a value model. Importantly, this requires no additional supervision, and our value model is trained on exactly the same data used for reward modeling. Building on this insight, we introduce \emph{Decoupled Value Policy Optimization} (DVPO), a framework that pretrains a \emph{Global Value Model} (GVM) offline and freezes it as a universal critic for policy learning. The GVM provides stable, fine-grained credit assignment without critic drift or trajectory sampling. Experiments across MT-Bench, Alpaca-Eval, and Arena-Hard demonstrate that DVPO matches or surpasses state-of-the-art RLHF methods. These results highlight RLHF can be reframed as policy-only optimization guided by a single pretrained value model. The implementation code for our method is available in \url{https://github.com/microsoft/DKI_LLM/tree/main/dvpo}

Applications · Language, Speech and Dialog

Heyang Gao, Zexu Sun, Erxue Min, Hengyi Cai, Shuaiqiang Wang, Dawei Yin, Xu Chen

Large Language Models (LLMs) as autonomous agents are increasingly tasked with solving complex, long-horizon problems. Aligning these agents via preference-based methods like Direct Preference Optimization (DPO) is a promising direction, yet it faces a critical granularity mismatch. Trajectory-level DPO provides stable signals but blur where credit should be assigned within long trajectories, whereas step-level DPO offers fine-grained supervision but can be statistically noisy and data-inefficient when Monte Carlo rollouts are limited, and can be hard to fully exploit multi-step structured behaviors that only reveal their effect over several actions. To balance this trade-off, we introduce **H**ierarchical **P**reference **L**earning (HPL), a hierarchical framework that optimizes LLM agents by leveraging preference signals at multiple, synergistic granularities. While HPL incorporates trajectory- and step-level DPO for global and local policy stability, its core innovation lies in group-level preference optimization guided by a dual-layer curriculum. Our approach first decomposes expert trajectories into semantically coherent action groups and then generates contrasting suboptimal groups to enable preference learning at a fine-grained, sub-task level. Then, instead of treating all preference pairs equally, HPL introduces a curriculum scheduler that organizes the learning process from simple to complex. This curriculum is structured along two axes: the group length, representing sub-task complexity, and the sample difficulty, defined by the reward gap between preferred and dispreferred action groups. Experiments on three challenging agent benchmarks show that HPL outperforms existing state-of-the-art methods. Our analyses demonstrate that the hierarchical DPO loss effectively integrates preference signals across multiple granularities, while the dual-layer curriculum is crucial for enabling the agent to solve a wide range of tasks, from simple behaviors to complex multi-step sequences.

Optimization · Large Scale, Parallel and Distributed

Muqing Liu, Chongjie Si, Yuheng Jia

Large pre-trained models achieve remarkable success across diverse domains, yet fully fine-tuning incurs prohibitive computational and memory costs. Parameter-efficient fine-tuning (PEFT) has thus become a mainstream paradigm. Among them, Low-Rank Adaptation (LoRA) introduces trainable low-rank matrices and shows strong performance, nevertheless, its fixed-rank design limits flexibility. Dynamic rank allocation methods mitigate this issue by pruning redundant directions; however, they often rely on heuristic, element-level metrics that globally sort rank directions without matrix-wise distinction, and they lack mechanisms to expand capacity in layers requiring additional adaptation. To overcome these limitations, we propose FlexLoRA, an entropy-guided flexible low-rank adaptation framework that (i) evaluates matrix importance via spectral energy entropy, (ii) supports rank pruning and expansion under a global budget, and (iii) employs zero-impact initialization for newly added singular directions to ensure stability. By addressing granularity, flexibility, and stability limitations, FlexLoRA provides a more principled solution for PEFT. Extensive experiments show that FlexLoRA consistently outperforms state-of-the-art baselines across benchmarks.

Optimization · Large Scale, Parallel and Distributed

Ying Yuan, Pengfei Zuo, Bo Wang, Zhangyu Chen, Zhipeng Tan, Zhou Yu

In large language model (LLM) serving, reusing the key-value (KV) cache of prompts across requests is a key technique for reducing time-to-first-token (TTFT) and lowering serving costs. Cache-affinity scheduling, which co-locates requests with the same prompt prefix to maximize KV cache reuse, often conflicts with load-balancing scheduling, which aims to distribute requests evenly across compute instances. Existing schedulers struggle to reconcile this trade-off, as they operate within a single mapping space, typically applying cache-affinity routing to a subset of requests and load-balanced routing to the rest, without a unified solution to achieve both goals. To overcome this limitation, we propose DualMap, a dual-mapping scheduling strategy for distributed LLM serving that simultaneously enables cache affinity and load balancing. The key idea of DualMap is to map each request to two candidate instances using two independent hash functions based on the request prompt, and then intelligently select the better candidate based on current system states. This design increases the likelihood that requests with shared prefixes are co-located, while evenly dispersing distinct prefixes across the cluster via ``the power of two choices''. To make DualMap robust under dynamic and skewed real-world workloads, we incorporate three techniques: 1) SLO-aware request routing, which prioritizes cache affinity but switches to load-aware scheduling when TTFT exceeds the SLO, enhancing load balance without sacrificing cache reuse; 2) hotspot-aware rebalancing, which dynamically migrates requests from overloaded to underloaded instances, mitigating hotspots and rebalancing the system; 3) lightweight dual-hash-ring scaling, which leverages a dual-hash-ring mapping to support fast and low-overhead instance scaling without costly global remapping. Experiments on real-world workloads show that DualMap improves effective request capacity by up to 2.25$\times$ under the same TTFT SLO constraints, compared with the state-of-the-art work.

Optimization · Non-Convex

Fanqi Wang, Weisheng Tang, Landon Harris, Hairong Qi, Dan Wilson, Igor Mezic

This paper centers around a novel concept proposed recently by researchers from the control community where the training process of a deep neural network can be considered a nonlinear dynamical system acting upon the high-dimensional weight space. Koopman operator theory (KOT), a data-driven dynamical system analysis framework, can then be deployed to discover the otherwise non-intuitive training dynamics. Taking advantage of the predictive power of KOT, the time-consuming Stochastic Gradient Descent (SGD) iterations can be then bypassed by directly predicting network weights a few epochs later. This "predictive training" framework, however, often suffers from gradient explosion especially for more extensive and complex models. In this paper, we incorporate the idea of "differential learning" into the predictive training framework and propose the so-called "predictive differential training" (PDT) for accelerated learning even for complex network structures. The key contribution is the design of an effective masking strategy based on a dynamic consistency analysis, which selects only those predicted weights whose local training dynamics align with the global dynamics. We refer to these predicted weights as high-fidelity predictions. DT also includes the design of an acceleration scheduler to adjust the prediction interval and rectify deviations from off-predictions. We demonstrate that PDT can be seamlessly integrated as a plug-in with a diverse array of existing optimizers (SGD, Adam, RMSprop, LAMB, etc.). The experimental results show consistent performance improvement across different network architectures and various datasets, in terms of faster convergence and reduced training time (10-40%) to achieve the baseline's best loss, while maintaining (if not improving) final model accuracy. As the idiom goes, a rising tide lifts all boats; in our context, a subset of high-fidelity predicted weights can accelerate the training of the entire network!

Daniel Tan, Anders Woodruff, Niels Warncke, Arun Jose, Maxime Riché, David Demitri Africa, Mia Taylor

Language model finetuning often results in learning undesirable traits in combination with desired ones. To address this, we propose inoculation prompting: modifying finetuning data by prepending a short system-prompt instruction that deliberately elicits the undesirable trait. At test time, we evaluate without the instruction; inoculated models have much lower expression of the trait than models trained with unmodified training data. Inoculation is selective: in a toy setting where assistant responses are always in Spanish and ALL-CAPS, an appropriate inoculation (e.g., "You always speak in Spanish.") teaches the model to capitalize responses while still responding in English. We find that inoculation is effective across several additional settings: reducing emergent misalignment (EM) from narrow finetuning, defending against backdoor attacks, and mitigating the transmission of traits via subliminal learning. Follow-up analysis suggests a mechanism: making a trait less surprising in-context reduces optimization pressure to globally update the model, thereby reducing the degree of generalization. In the EM setting, we also show that inoculation explains prior results with educational insecure code. Beyond demonstrating a simple and effective technique for selective learning, our results contribute to a better conceptual understanding of how and why language models generalize.

Computer Vision · Everything Else

Guijie Wang, Tong Lin, Yifan Bai, Anjia Cao, Shiyi Liang, Wangbo Zhao, Xing Wei

Inference speed and tracking performance are two critical evaluation metrics in the field of visual tracking. However, high-performance trackers often suffer from slow processing speeds, making them impractical for deployment on resource-constrained devices. To alleviate this issue, we propose $\textbf{FARTrack}$, a $\textbf{F}$ast $\textbf{A}$uto-$\textbf{R}$egressive $\textbf{T}$racking framework. Since autoregression emphasizes the temporal nature of the trajectory sequence, it can maintain high performance while achieving efficient execution across various devices. FARTrack introduces $\textbf{Task-Specific Self-Distillation}$ and $\textbf{Inter-frame Autoregressive Sparsification}$, designed from the perspectives of $\textbf{shallow-yet-accurate distillation}$ and $\textbf{redundant-to-essential token optimization}$, respectively. Task-Specific Self-Distillation achieves model compression by distilling task-specific tokens layer by layer, enhancing the model's inference speed while avoiding suboptimal manual teacher-student layer pairs assignments. Meanwhile, Inter-frame Autoregressive Sparsification sequentially condenses multiple templates, avoiding additional runtime overhead while learning a temporally-global optimal sparsification strategy. FARTrack demonstrates outstanding speed and competitive performance. It delivers an AO of 70.6\% on GOT-10k in real-time. Beyond, our fastest model achieves a speed of 343 FPS on the GPU and 121 FPS on the CPU. Source code is available at: https://github.com/MIV-XJTU/FARTrack.git

Applications · Chemistry and Drug Discovery

Michael Sun, Weize Yuan, Gang Liu, Wojciech Matusik, Marinka Zitnik

Protein structure is central to biological function, and enabling multimodal protein models requires joint reasoning over sequence, structure, and function. A key barrier is the lack of principled protein structure tokenizers (PSTs): existing approaches fix token size or rely on continuous vector codebooks, limiting interpretability, multi-scale control, and transfer across architectures. We introduce GeoBPE, a geometry-grounded PST that transforms continuous, noisy, multi-scale backbone conformations into discrete ``sentences'' of geometry while enforcing global constraints. Analogous to byte-pair encoding, GeoBPE generates a hierarchical vocabulary of geometric primitives by iteratively (i) clustering Geo-Pair occurrences with k-medoids to yield a resolution-controllable vocabulary; (ii) quantizing each Geo-Pair to its closest medoid prototype; and (iii) reducing drift through differentiable inverse kinematics that optimizes boundary glue angles under an $\mathrm{SE}(3)$ end-frame loss. GeoBPE offers compression ($>$10× reduction in bits-per-residue at similar distortion rate), data efficiency ($>$10× less training data), and generalization (maintains test/train distortion ratio of $1.0-1.1$). It is architecture-agnostic: (a) its hierarchical vocabulary provides a strong inductive bias for coarsening residue-level embeddings from large PLMs into motif- and protein-level representations, consistently outperforming leading PSTs across $12$ tasks and $24$ test splits; (b) paired with a transformer, GeoBPE supports unconditional backbone generation via language modeling; and (c) tokens align with CATH functional families and support expert-interpretable case studies, offering functional meaning absent in prior PSTs.

Reinforcement Learning · Planning

Kai Zhang, Jingjing Gu, Qiuhong Wang

Dynamic Path Planning (DPP) in urban road networks faces fundamental challenges, as traffic conditions change rapidly over time and often render planned routes ineffective. Reinforcement Learning (RL) provides an effective way to adaptively handle such uncertainties by incorporating traffic dynamics into state, but its performance crucially depends on how these dynamics are represented. Existing approaches either rely on global traffic information, which ensures decision completeness but suffers from redundancy and high computational cost, or oversimplified local features, which are efficient but often omit critical dynamics and lead to suboptimal paths. To address this, we propose a Dynamics Feature Representation (DFR) framework that progressively refines global traffic dynamics into compact features for RL-based DPP. Specifically, we introduce a policy attention mechanism that identifies a core subset of global dynamics by extracting the top-k shortest paths, and further constructs node-related local features by intersecting with n-hop neighborhoods, enabling near-optimal policy learning. Theoretical analysis demonstrates that DFR guarantees state completeness, while empirical results confirm that, compared to classical baselines and standard RL methods, DFR significantly improves path planning performance and accelerates convergence. This work highlights the central role of feature representation in RL-based DPP and proposes a general framework that balances information sufficiency with computational efficiency, paving the way for scalable dynamic decision-making in real-world transportation systems.